Kirk is a poor fighter compared to comic MAs like Cap. He also hasn't studied Spider-Man like Cap has, and Peter won't have the same hero worship for him that he does for Steve, so all in all, Tiberius won't do as well against Spidey HtH as Cap would.

Granted, you gave him a phaser as well, but I think Spidey would be able to avoid his shots and disarm him pretty easily.